Finite and infinitesimal rigidity with polyhedral norms
Kitson, D.
Original · EN
We characterise finite and infinitesimal rigidity for bar-joint frameworks in Rᵈ with respect to polyhedral norms (i.e. norms with closed unit ball P a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in Rᵈ which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of the framework is used to characterise infinitesimal rigidity in Rᵈ in terms of monochrome spanning trees. An analogue of Laman's theorem is obtained for all polyhedral norms on R².
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